for a minimal reduction \(J\subseteq I.\) 
Since then many attempts have been made to achieve a bound of similar character in higher dimension. For instance, the bound in (REF ) holds in all dimensions if \(\operatorname{depth}G(I)\ge d-2\)  [1]} or if \(e_1(I)-e_0(I)+\lambda (R/I)=1\)  [2]}. Another case is when \(I\subseteq k[x,y,z]\)  is of codimension 3 generated by five quadrics [3]}. However, no example is known to counter the
relation in (REF )
in higher dimension. In this paper, our objective is to find bounds for \(r_J(I)\)  in dimension three involving higher Hilbert coefficients. We prove the following generalization of Rossi's result [1]} in dimension three:
